Discount rates: A boring thing you should know about (with otters!)

How much is it worth to us today to avoid climate disruption later this century? To understand how that question has typically been answered, you need to understand what economists call “discount rates,” key parameters in the economic models used to assess climate policy costs. Such models inform policymaking and shape conventional wisdom, but their use of discount rates has led them to lowball the threat and recommend insufficient action to meet it.

You see my problem here: You’re already bored as sh*t. And the literature on this is as voluminous as it is technical. You could be much more bored. Trust me.

But don’t give up! It really does matter. Understanding discount rates will help you understand the climate-policy landscape — not only the technical details, but the struggle over values that lurks underneath them.

So stick with me. To help counter the soporific effects of the subject, I shall endeavor to explain it in a lively, accessible fashion. Failing that, I’ll use otters.

OK! Let’s recall a vexing fact about climate change: There’s a substantial time lag between causes and effects. Greenhouse gases emitted today affect global temperatures in 50 years or so, just as we’re experiencing temperature rise caused by emissions 50 years ago. This time lag complicates efforts to do something about the problem, to say the least, as people are not generally temperamentally inclined to sacrifice now to gain benefits (or to avoid costs) 50 years down the road. We prefer instant gratification; we’re pretty myopic.

The policy challenge, then, is to pull those damages out of the future and into the present. We need to amplify that distant signal so that it is heard in everyday economic decision-making.

The preferred way to achieve this goal is to put a price on carbon, via a tax or a cap. The carbon price is meant to reflect the damages emissions will cause later, or, in dork-speak, to “internalize the externalities.”

To do this properly — to figure out the “right” price for a ton of CO2 emissions — we have to answer two questions. One, how much damage will a ton of carbon do? And two, how much is it worth to us to avoid that amount of damage?

Climate science can help answer the first question, though it can’t, and likely never will be able to, give us a precise figure. Especially at regional or more granular levels, precision is impossible given the limitations of current science and the inherent complexities of the global atmospheric system. But if we want a figure or range of figures to work with, we can choose from the center of the probability distribution and get something that’s “good enough for government work,” as they say.

The second question is trickier. The physical sciences cannot answer it. How much future climate mitigation is worth to us today — what’s called the social cost of carbon — is a matter for economics and ethics. And it’s here that discount rates enter the picture. We must prepare ourselves with an otter.

To get our heads around discount rates, let’s first focus on how they work in individual decision-making. There are two concepts to grasp here: revealed time preferences and opportunity costs. (Hey, I just gave you an otter.)

Here’s a thought experiment. Say I gave you a choice: I’ll give you $100 today or $100 in 10 years. You’d choose today, obviously. What if the choice was $70 today or $100 in 10 years? Hm … tougher. $50 today?

If you choose $50, you’re saying you value dollars today twice as much you value as dollars 10 years from now.

The degree to which you prefer present benefits (money today) over future benefits (money in the future) is known as your “revealed time preference.” It is “revealed” in that it is reflected in your savings and investment decisions, even if it is never articulated.

Now, here’s another scenario. What would you pay today to avoid $100 in damage to your car a year from now? In making this decision, you would think about what else you could do with the money in the meantime. “Hm, I could put $100 in a bank account and, at a 3 percent interest rate, in a year I’d have $103. I could pay off the repair bill and pocket $3 in profit!” In a situation of 3 percent interest rates, it’s only worth $97 to you today to avoid $100 in damage a year from now. Otherwise you could make more by investing the money differently. What if the $100 in damage was in 10 years? Then it would only be worth $67. How about 30 years? Just $41.

How much an investment pays relative to other uses of the same resources is known as its “opportunity cost” — for every investment, you choose to forego other opportunities.

Revealed time preference and opportunity costs together lead us to discount the value of future benefits. Think of it like compound interest, only run in reverse; to an investor today, returns lose some percentage of their “net present value” each year they recede into the future.

That percentage, the amount that a benefit declines in value each year into the future it extends, is the discount rate. In financial transactions, the discount rate is typically set somewhere around prevailing market interest rates.

OK! We know what discount rates are and how they factor into savings and investment decisions. So far so good. Things get a little stickier and more complicated when it comes to climate change, though. So let’s take a quick otter break.

Why are discount rates a vexed subject when it comes to climate change? Mainly because climate change involves long time spans and globe-spanning geography — and therefore multiple generations and multiple societies.

Let’s focus on the time spans. Consider: If we have a discount rate of 3 percent — which is a fairly representative rate in economics — and we face $100 of climate damages in 2100 (roughly 87 years from now), it is worth about $7 to us to avoid it. Hardly anything.

To make it more vivid, imagine climate change were on track to cause $5 trillion ($5,000,000,000,000) in damages by the end of the century. That’s an unthinkably large number. (Go ahead, try to think about it.) And it represents unthinkable suffering. But at a discount rate of 3 percent, it would be worth just $382 billion to us today to avoid it. For perspective, that’s a little more than half the annual U.S. military budget.

It starts to seem a little absurd. And it gets even crazier if you apply a discount rate of 5 percent, as some people suggest (5 percent is roughly the return on U.S. Treasury bills). That would mean avoiding $5 trillion in damages in 2100 is worth about $72 billion today. By comparison, that’s just over what China expects to invest in high-speed rail this year.

So you see: If we use discount rates in the 3-5 percent range, we can’t justify spending much of anything on climate policy today. And that’s what some popular modeling shows. Yale economist William Nordhaus, for instance, uses a discount rate of 3 percent, so his modeling tells us that all we need at the moment is a modest (around $5/ton) carbon tax. (Or, put another way, the social cost of carbon is $5 in today’s dollars.) [UPDATE: OK, this is slightly off. Nordhaus’s optimal CO2 price was $7.40 a ton in 2005, meant to rise 2 or 3 percent a year, so it would be around $9 or $10 today. Still pretty low.]

If that doesn’t jibe with your moral intuitions, you’re not alone. U.K. economist Nicholas Stern, in his famed Stern Review, used largely the same scientific data as Nordhaus, but with a discount rate of just 0.1 percent. [UPDATE: Stern used 0.1 percent for time preference but 1.4 percent for the full discount rate; my bad.] Not surprisingly, Stern’s modeling suggests that the social cost of carbon is closer to $85 a ton and rising.

Again, these two, the “delayer” and the “alarmist,” do not disagree on the scientific facts of climate change. They just disagree about how much we should value damages to future people. That’s the difference between apathy and panic.

So what should the discount rate be? What number should economists use when modeling climate change policy? And how do we decide? Before we get into that heaviness, we need a little otter.

So who’s right about the discount rate, Nordhaus or Stern? Suffice to say, this is a subject of vigorous dispute. If you want to dig in, you have many long and excruciatingly boring journal articles to choose from. I will merely scratch the surface here. Long story short: There’s no “right” answer, only a judgment call.

Those who argue for a higher discount rate (in the 3-5 percent range), like Nordhaus himself [PDF], favor what they see as a descriptive rather than prescriptive approach. Ours is not to ask what the discount rate “should” be, ours is but to determine people’s actual time preferences as revealed in their everyday market behavior (i.e., look to prevailing market interest rates). It’s the only way to avoid “paternalism,” smuggling moral judgments into economics.

One of their primary assumptions is that people in the future will be richer than us, and thus better prepared to deal with climate damages. If it’s a choice between making them richer and reducing their climate damages, we should generally lean toward making them richer. Only if climate mitigation investments offer a rate of return higher than prevailing interest rates are they worthwhile. Otherwise, we’d be better off just putting the money in a bank.

For my part, I find arguments for a lower (or even zero) discount rate much more persuasive. This does not strike me as an area where “paternalism” can or should be avoided. We’re literally the parents (and grandparents) in this situation!

First, let’s discuss this notion that people’s revealed time preferences are a kind of neutral baseline discount rate, devoid of ethical judgment. I like this point from professor Paul Kelleher, who wrote a short review on “energy policy and the social discount rate” [PDF]. He’s responding here to Martin Weitzman, who argues that the social discount rate should reflect prevailing interest rates (i.e, prevailing time preferences):

Weitzman is surely correct that prevailing interest rates reveal ethically relevant information. But it is information about how individuals, acting as individuals and largely in their own interests, weight present versus future well-being. However, the social discount rate should reflect explicitly moral, other-regarding judgments about the relative importance of well-being that exists far into the future. It is by no means clear that individuals’ self-regarding behavior yields any insight whatsoever about what even those same individuals believe we owe to future generations.

Right. It’s one thing for an investor to make decisions about how much future value she will sacrifice for present value. It’s another for her to make decisions about how much value future people will sacrifice for her present value. Those are decisions that affect other people, paradigmatically ethical decisions, so it is no longer her discount rate alone that’s relevant. There’s no avoiding ethical judgment here.

More arguments against high discount rates can be found in this post from NRDC chief economist Laurie Johnson (to whom we will return later). I’ll share her top-line points.

First:

An increasingly disrupted climate may hamper economic productivity, causing economic growth rates to deviate below their historical trajectories. If worse-case climate risks materialize, climate change could even reverse economic growth. In that instance, people in the future would be poorer than people today, not wealthier.

This is the big one for me. Recent science is pointing more and more strongly to the danger of 4, 5, even 6 degree Celsius temperature rise by 2100, while at least some climate scientists are warning that “economic growth cannot be reconciled with the breadth and rate of impacts as the temperature rises towards 4°C and beyond.” Avoiding impacts that scientists characterize as dangerous and irreversible will require heroic effort.

Are we really so sure economic growth will continue as it has during our age of energy (and carbon) abundance? It’s always seemed to me that economists have near-religious faith in economic growth; models show everyone getting richer because models reflect that faith. But in an age of climate disruption, amidst “long tail” risks of truly catastrophic, even species-threatening damages, it seems insanely risky to try to dial the economic knobs to maximize returns. Surely a more precautionary approach, akin to purchasing insurance, is appropriate.

More from Johnson:

Private investors (and hence market returns) do not take into account pollution externalities resulting from production, such as the depreciation of natural capital (e.g., loss of natural habitats to development and pollution) and public health damages, or other potentially negative social impacts related to economic production, such as inequality. They therefore tend to overestimate the impact growth has on real social welfare.

Yes. Private investment decisions are made entirely within market rules, but some market rules may be maladapted to social welfare, especially future social welfare. (“You can emit carbon for free,” for instance, seems like a rather imprudent rule.) Market growth in these circumstances only exacerbates maladaption. Social and ethical decisions must encompass a broader perspective than markets can provide.

Johnson adds:

Even if income grows under a changing climate, it is unlikely that the people most harmed by climate change will be the recipients of that growth.

The more provocative way to put this point is that global economic growth is entirely consistent with the loss of the entire African continent to drought and disease. After all, Africa doesn’t contribute much to global GDP.

This gets back to climate change’s global reach. When Americans say “future generations” will benefit from our money more than our mitigation, we should be clear that we’re talking about future generations of us, the people with the wealth necessary to weather climate disruption. Future generations of the poor and vulnerable will suffer far more than they otherwise would have. We will be displacing suffering temporally and geographically. Call it the “geographical discount rate.”

And finally, this old chestnut:

Money isn’t everything.

True!

Say you could ask the people of 2100 (some of whom may be your children or grandchildren), “would you rather inherit $1 trillion in cash or $1 trillion worth of avoided drought, storm, and famine?” Which do you think they would choose?

They will have lost biodiversity, up to half the species on the planet. They will have lost millions of acres of old-growth and tropical forest, most of the world’s coral reefs, and the bulk of world’s annual sea ice. Those things will never return, not in time spans relevant to our species. The natural world that has provided us sustenance since we were primates can not be restored once it’s gone. And there’s more to the biosphere than the “services” it provides humans. Some damages cannot be captured in dollar terms.

Anyway, those are the arguments for a low-or-zero discount rate. Or at least some of the arguments. Sounds like time for an otter.

Say we’re convinced by these arguments and adopt a low discount rate, a social cost of carbon that reflects that low discount rate, and a price on carbon that reflects our new social cost of carbon. What are the consequences?

Well, for one thing, renewable power immediately becomes cheaper than fossil-fuel power, including natural gas.

That’s the sexy conclusion. Let’s run through the argument, which is in two parts.

First is a new paper out in the Journal of Environmental Studies and Sciences, by the aforementioned Laurie Johnson and her colleague Chris Hope of Cambridge. In it, they argue that the U.S. government has substantially underestimated the social cost of carbon, which threatens to distort future regulatory and legislative decisions.

“Say whaaa?” you ask. “The U.S. government has put on a price on carbon?” Why yes! Here’s the situation:

In 2010, as part of a rulemaking on efficiency standards, the U.S. government published its first estimates of the benefits of reducing CO2 emissions, referred to as the social cost of carbon (SCC). Using three climate economic models, an interagency task force concluded that regulatory impact analyses should use a central value of $21 per metric ton of CO2 for the monetized benefits of emission reductions.

The problems with the economic models the government used are twofold, say Johnson and Hope. The first, as you likely guessed, is about discount rates. The government instructed the task force to consider only three discount rates: 2.5, 3, and 5 percent. Three percent was considered the mean, or “central” value.

As we’ve seen, that might make sense for costs and benefits confined to a single generation, but across generations, a rate that high is not ethically justified. Even the government agrees: The Office of Management and Budget has official guidelines [PDF] on the use of discount rates in inter-generational cost-benefit analysis. It says they can range from 1 to 3 percent. Yet somehow 3 ended up as the task force’s “mean.”

They also made another change. The task force models treat damages equally across geographic regions. They use a geographical discount rate of zero; a dollar of damage here is equal to a dollar of damage there. But fairness and decency would indicate that a dollar of damages in a poor region is worse — reduces human well-being more — than a dollar of damages in a rich region.

So Johnson and Hope added “equity weights” to regional damages, based on relative income levels.

[UPDATE: To clarify: Johnson and Hope ran the models with low discount rates, then they ran a few with equity weights separately, for illustrative purposes. The two tweaks were not combined in any model runs; if they had been, the estimates of SCC would have been even higher.]

With those changes (effectively reflecting Stern’s assumptions rather than Nordhaus’s), the authors found a social cost of carbon “2.6 to over 12 times larger” than the $21 central estimate of conventional models, which indicates that “regulatory impact analyses that use the government’s limited range of SCC estimates will significantly understate potential benefits of climate mitigation.” That matters a lot, especially at a time when EPA carbon emissions are subject to such intense political scrutiny.

In a supplemental piece, Johnson compares the levelized costs of different forms of power in light of her new social cost of carbon.

Overall, the analysis shows that if the well-being of future generations is properly taken into consideration, the benefits of cleaner electricity sources are greater than their upfront costs, both for new generation, and for replacing our dirtiest plants. In contrast, using the government’s estimate of CO2 damage costs tends to favor dirtier energy sources, and an ever riskier climate. [my emphasis]

So if you take equity into account and use a low discount rate — that is, if you choose to treat future generations and vulnerable peoples with moral regard — clean energy is already cheaper than dirty energy.

That’s something I wish I could get people to understand: The “cost” of a form of energy is not an objective property of the universe, measured by a market cost-o-meter. It’s a social construct, the result of assumptions built into the way we calculate value. Those assumptions are not holy writ. They can be contested.

Along those lines, check out this response to Johnson’s work from one of the modelers involved in the government commission:

Michael Greenstone, a former chief economist for the president’s Council of Economic Advisers who helped create the $21 price tag back in 2010, said he stands by the 2010 analysis.

“I’m not overwhelmed by the opinions of two people, experts as they may be, about what the proper assumptions are, not compared to the collective effort of a dozen federal agencies and leading experts from the wide variety of disciplines that have insight into the climate change problem,” Dr. Greenstone said. “Calculating the social cost of carbon requires many, many assumptions.”

“What the authors of this study are highlighting is that as you change those assumptions, you can make the number go up or down,” he said. “There are other people that believe the discount rate should be even higher, which would lead to a substantially smaller social cost of carbon.” he said.

It’s true that there are many assumptions involved in determining a social cost of carbon. What’s also true is that many of those assumptions are based, in part, on moral judgments.

As a polity, how should we make those kinds of judgments? Frank Partnoy, a professor of law and finance at the University of San Diego, makes the right point:

“Ultimately, we can’t rely on only numbers — we have to make really hard value judgments,” Dr. Partnoy said. “We should stop pretending this is a science and admit it is an art and talk about this in terms of ethics and fairness, not what we can observe in the markets.”

That, to me, is the key take-home message about discount rates: They are social and ethical disputes being waged under cover of math, as though they are nothing but technical matters to be determined by “experts.” But social and ethical judgments should be made in an open, transparent way, not buried in models as inscrutable parameters.

I mean, we’re talking about how much we value our children and grandchildren. Surely that’s a matter for democratic discussion and debate!

Now you know what discount rates are and you can participate in those debates. You deserve an otter.